Customers of Ulster Bank could end up going without a fully functioning bank account for an entire month, the bank's parent company Royal Bank of Scotland admitted on Wednesday.

More than a fortnight after a technical problem sent the bank's computers into disarray, many customers are still experiencing difficulties accessing accounts and processing payments, with some reporting that vast sums of money have disappeared in the system.

In a statement RBS said it expected next week to be the final week of "significant delays", but warned that some customers could still be experiencing problems almost a month after the original fault.

"It is our expectation that by the week of the 16 July the vast majority of customers will return to a normal service, barring any residual reconciliation required," it said.

It was important to note, RBS added, that "it is not, and has never been, the case that all Ulster Bank services are unavailable", pointing out that it had now cleared payments "which will allow customers to see a material improvement in the information they have".

Among Ulster Bank's more than 100,000 customers is James Conlon, a businessman, who told the BBC that £50,000 of payments to his firm had not been credited to his account. That money has now turned up, but other customers are still waiting for their money.

On Twitter, a user writing under the name JoooyG wrote: "Oh thanks ulster bank for my credit card statement … It would help if you decided to put my wages from 2 weeks ago into my account first."

The chief executive of Ulster Bank, Jim Brown, apologised to customers, who he said had every right to be frustrated, adding: "Our efforts to fix this are paying off, and over the last few days we have been able to gain a much clearer picture about when we expect all systems to be largely back to normal.

"We expect gradual and significant improvements for our customers and each day we will see more transactions processing, fewer problems with our systems, and less inconvenience for our customers." Brown thanked other banks who had worked with his own to help process payments.

The Democratic Unionist Party deputy leader, Nigel Dodds, who is leading the delegation said: "Thousands of people across Northern Ireland are experiencing severe difficulties because of the long-running saga in Ulster Bank.

"Customers have been particularly angered by the silence which has emanated from Ulster Bank during this crisis."

Dodds said customers were angry that it appeared NatWest customers had been prioritised as the bank attempted to clear the backlog of payments.